Estudiantes completed an unhappy night for Argentine sides when they were thrashed 3-0 by Brazil's Cruzeiro in the evening's other game.
Peru captain Solano, who returned home after 12 years when he joined Universitario at the start of this year in a surprise move, controlled the midfielder as Universitario dominated the first half of the Group Eight game in Lima.
The former Newcastle United, Aston Villa and West Ham player was involved in the move which led to the 19th minute penalty, launching the ball to Calheira, who was upended by Jonathan Bottinelli.
Bottinelli was sent off and Solano calmly converted the penalty.
Solano was also close to a second near the end after a neat one-two but his shot was saved by Agustin Orion.
It was a welcome victory for Peru, whose teams have regularly struggled in recent editions of the tournament.
Cruzeiro scored three times in 10 minutes in their win at the Mineirao in Belo Horizonte.
Fernandinho broke the deadlock with a 62nd minute penalty then Kleber, who come on as a substitute in the 60th minute, scored twice in quick succession.
Kleber completed an eventful evening when he was sent off in the 84th minute for a crude tackle on Juan Sebastian Veron.
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